Probably has nothing to do with the pixels, as speculated in your teardown. It is more likely based on how we synthesize 3D from multiple cues. People who have the use of only one eye still see the world in 3D. And, the head tracking needs of dynamic perspective seem very similar to this:

http://johnnylee.net/projects/wii/

See the third project down, the one about 3D? It is uncanny to watch that video, you share the illusion on your screen even though your head is not being tracked. It seems the brain is able to adopt someone else's perspective and create the illusion. Pretty cool.

Comparing only the price will not be a good idea for Amazon Fire, this is a special phone that is launched for the Amazon lovers.

As the article says "Amazon has undoubtedly invested heavily in software features that are not included in this BOM costing estimate, most notably the software behind the Dynamic Perspective display feature"

Also the Amazon FireFly is another great feature that comes with this phone. It turns the phone into a scanner that redirects you to the products available on the Amazon store.

Yes but the premium that Amazon is charging, I also think is very high.

Thanks for this post. It is nice to have the information on the BoM cost of Fire phone. I was amazed to see that while Amazon has prices Fire at @ USD 649, the Chinese manufacture Xiaomi has priced Mi3 at ~USD 249 (in India). There features offered by Mi3 is almost the same as those of Fire. Hence I would assume the BoM cost of Mi3 similar as that of Fire. It would be interesting to have the same teardown exercise done on Mi3... :)